Clinical correlates of graph theory findings in temporal lobe epilepsy

Abstract

Purpose

Temporal lobe epilepsy (TLE) is considered a brain network disorder, additionally representing the most common form of pharmaco-resistant epilepsy in adults. There is increasing evidence that seizures in TLE arise from abnormal epileptogenic networks, which extend beyond the clinico-radiologically determined epileptogenic zone and may contribute to the failure rate of 30–50% following epilepsy surgery. Graph theory allows for a network-based representation of TLE brain networks using several neuroimaging and electrophysiologic modalities, and has potential to provide clinicians with clinically useful biomarkers for diagnostic and prognostic purposes.

Methods

We performed a review of the current state of graph theory findings in TLE as they pertain to localization of the epileptogenic zone, prediction of pre- and post-surgical seizure frequency and cognitive performance, and monitoring cognitive decline in TLE.

Results

Although different neuroimaging and electrophysiologic modalities have yielded occasionally conflicting results, several potential biomarkers have been characterized for identifying the epileptogenic zone, pre-/post-surgical seizure prediction, and assessing cognitive performance. For localization, graph theory measures of centrality have shown the most potential, including betweenness centrality, outdegree, and graph index complexity, whereas for prediction of seizure frequency, measures of synchronizability have shown the most potential. The utility of clustering coefficient and characteristic path length for assessing cognitive performance in TLE is also discussed.

Conclusions

Future studies integrating data from multiple modalities and testing predictive models are needed to clarify findings and develop graph theory for its clinical utility.

1. Introduction

Temporal lobe epilepsy (TLE) is the most common form of pharmaco-resistant epilepsy requiring surgical resection. However, the epileptogenic zone, the area of cortex whose resection is necessary and sufficient to stop seizure activity, often differs from the epileptogenic lesion visible on magnetic resonance imaging.¹ Currently, 30–50% of patients who undergo TLE surgery fail to achieve seizure freedom at 5 years.² Although reasons for surgical failure are unclear, they are likely related to imperfect identification of the epileptogenic zone.^3,4 Increasing evidence suggests that TLE is a network disease leading to temporal and extratemporal structural and functional changes,^5–8 and that seizures in focal epilepsy arise from abnormal epileptogenic networks rather than from focal sources. This has reignited an interest in the study of the network structure of TLE, as targeting key network components is a potential direction in achieving control of epilepsy. Graph theory provides a promising method to identify these components.

There are several methods to study brain networks, collectively referred to as connectomics.⁶ Specific analysis methods have been developed to study both structural and functional network structures, including tractography for diffusion tensor imaging (DTI), and seed-based methods and independent component analysis for functional connectivity magnetic resonance imaging (fcMRI). Unlike techniques based solely on pair-wise comparisons, graph theory takes into account the full network structure by providing a simple model of the true underlying brain connectome, represented by a collection of nodes and edges.⁹ By reducing the complex network structure of the brain into a set of parameters which characterize specific topological properties of the network, it enables the study of individual nodes as well as the network as a whole.¹⁰ Early encouraging findings suggest that conversion of modality specific data to topologic measures by graph theory analysis may improve clinical interpretability.¹¹ These metrics constitute ideal potential biomarkers due to their easily accessible clinical interpretability in addition to ability in capturing topological aspects of both the brain network and individual regions. A summary of the biological interpretation of graph theory metrics commonly encountered in TLE studies is provided in Table 1. Fig. 1 provides an overview of the typical graph theory analysis pipeline which is used to evaluate topological properties of TLE brain networks.

Table 1.

Definition and clinical interpretation of common graph theoretic measures examined in this review.

Common correlation measures
Small world measures
Clustering coefficient	Measure of local connectivity (i.e., the “cliquishness” of the network). Associated with efficient recurrent processing in closed feedback loops and efficient information exchange43
Characteristic path length	A measure of long-distance or “global connectivity,” as well as measure of network’s ability for serial information transfer.44 Inversely related to the how well the network is integrated.45 Lower path length has also been associated with higher IQ26
Small world index	Calculated from a normalized ratio of the clustering coefficient to the path length. A small-world index >1 indicates brain networks with small-world organization
Centrality measures
Betweenness centrality	Identifies nodes located on the most traveled paths,46 by measuring the number of shortest paths that pass through a node
Leverage centrality	Measures the extent to which a node’s immediate neighbors rely on it for information. Positive values indicate that a node is more highly connected than its neighbors, implying that the node acts as a “hub.” Negative values indicate that the node receives information from other more highly connected nodes46
Degree centrality (degree)	Measures how connected a region is to the rest of the network. Calculated as the number of edges by which a node is directly connected to other nodes in the network
Network hub	A node whose degree is larger than the average degree of the network. Identifies nodes which are connected to a large number of other nodes47,48 and which mediate many of the short path lengths between other nodes
Assortative hubs	Hubs that tend to connect to other hubs
Disassortative hubs	Hubs that tend to avoid other hubs
Other commonly used measures
Connectivity	Often estimated as the raw values of the association measure used to construct graph edges (e.g. Pearson correlation, partial correlation, synchronization likelihood, etc.)
Edge weight correlation	The extent to which the connections to one region have similar weights. High edge weight correlation is considered beneficial for information processing, due to increased information transport/.49 However, edge weight correlations which are too high increase vulnerability to seizures50
Outdegree	In a directed graph, this refers to the number of nodes that a given node points to, and reflects the number of outgoing connections. Nodes with high outdegree act as sources of information flow within a system10,18
Strength (mean absolute correlation)	Mean absolute value of the correlation of a node i to all other nodes
Assortativity coefficient	Measures the propensity of nodes in a network to connect to other nodes with a similar degree. Calculated as the level of correlation between the degree centrality of pairs of linked nodes.51 Positive values indicate connections with nodes with similar degree centrality; negative values indicate connections with nodes with dissimilar degree centrality
Graph index complexity	A measure of graph complexity introduced by 52. Provides quantification of the complexity of a graph by serving as a nonlinear indicator of high-frequency oscillations in epileptic signal
n-to-1 connectivity	Amount of information that a node receives from the rest of the network; provides a measure of nodal strength

Fig. 1.

Overview of graph theory analysis. Nodes and edges for the brain graph are first defined specific to each modality (a). Next, an adjacency matrix is constructed based on any of a variety of association measures (b). Values of the adjacency matrix are used to construct a graph of the brain network (c). Various graph theory metrics can then be calculated (d–f). In (d), the red node has four direct neighbors connected by the “edges” (black lines). The clustering coefficient of the red node can be calculated as the ratio of the number of existing connections between these direct neighbors (two) to the number of possible connections between these direct neighbors (six), or 1/3. In (e), the characteristic path length between the red and blue nodes is the least number of edges between them (two). In (f), there are two sets of interconnected neurons which form so-called “modules,” and are interconnected though the green “hub” through which most of the shortest path lengths pass in this network. SL = synchronization likelihood, PLI = phase lag index, DTF = directed transfer function. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

In this review, we discuss the current state of clinical utility for graph theory findings in TLE, including those relating to (1) diagnostic findings including lateralization and localization of TLE, (2) prediction of pre- and post-surgical seizure recurrence and cognitive performance, and (3) mechanisms of cognitive decline. A summary of these studies is provided in Table 2.

Table 2.

Summary of clinical findings. C = unnormalized clustering coefficient; L = unnormalized path length, γ = clustering coefficient; λ= characteristic path length; σ= small-world index.

	Modality	Study population	Graph metrics	Major findings	Significance
Bernhardt et al.19	MRI	122 drug-resistant TLE patients (63 left TLE, 59 right TLE), 47 controls	C, L, γ, λ, σ	Graph-theoretical analysis of MRI-based cortical thickness correlations. TLE patients showed increased path length and clustering coefficient, altered distribution of network hubs, and higher vulnerability to targeted attacks Both TLE patients and controls possess small-world topology. Increased clustering coefficient and path length associated with non seizure-free post-operative outcome. Longitudinal analysis demonstrated that network alterations intensify over time.	Prediction of post-surgical seizure performance
James et al.12	fMRI	7 left TLE, 8 right TLE, 23 controls	Strength, degree, leverage centrality, γ, betweenness centrality	Connectivity of ipsilateral hippocampus and parahippocampus is decreased in lateralized TLE	Biomarker for lateralizing epileptogenic focus
Vlooswijk et al.29	fMRI	41 cryptogenic epilepsy, 23 controls	L, C, local efficiency, global efficiency	Decreased γ and increased λ in TLE Decreased IQ associated with decreased γ in TLE	Mechanism of cognitive decline
Liao et al.13	fMRI	18 bilateral mTLE, 27 controls	Hubs, degree distribution, n-to-1 connectivity, C, L, γ, λ, σ	Increased connectivity within temporal, decreased connectivity within frontal and parietal and between frontal and parietal lobes in mTLE. Reduced connectivity of DMN areas in mTLE. Increased n-to-1 connectivity of bilateral rectal gyri, left medial orbital superior frontal gyrus, left middle temporal gyrus, right orbital inferior frontal gyrus, and right medial superior frontal gyrus in mTLE. Decreased C, decreased L in mTLE	Characterization of TLE with medial focus
Vaessen et al.30	DTI	39 cryptogenic epilepsy, 23 controls	L, C	Frontal/temporal lobe epilepsy with severe cognitive impairment have lower clustering coefficients and higher path lengths than healthy controls and patients with mild cognitive impairment. No difference in whole brain white matter volume between patients and controls. In patient group, decreasing clustering coefficient and increased path length are correlated with lower cognitive functioning.	Mechanism of cognitive decline
Douw et al.22	EEG	33 pharmaco-resistant TLE patients before and after IAP/Wada test (taken as a model for brain lesion)	γ, λ, σ, edge-weight correlation	Following amobarbital injection: γ decreased in all frequency bands. λ decreased in the θ- and lower α-bands. Shift toward more random network topology. Edge-weight correlation decreased in θ- and β-bands. Higher θ-band small-world index and increased upper α-band path length were associated with better memory score.	Post-surgical seizure prediction
Quraan et al.14	EEG	9 drug-resistant left TLE patients, 15 controls	Normalized efficiency, γ, σ	Largest differences from controls were in the θ (4–7 Hz) and α (10–13 Hz) bands. In the θ band: increased local processing (γ), increased small-world index (σ), deviations toward regular network. In the high α band: decreased local processing (γ), decreased small-world index (σ), deviations toward random network.	Biomarker for lateralizing epileptogenic focus
Bialonski and Lehnertz23	EEG	60 patients with focal epilepsy	Assortativity coefficient	Assortativity coefficient is decreased interictally, increases during the seizure, plateauing at the end of the seizure, and decreases after the seizure.	Prediction of seizure onset
Wilke et al.15	icEEG	25 neocortical intractable epilepsy patients	Betweenness centrality	Betweenness centrality was found to correlate with the location of the resected cortical regions in patients who were seizure-free following surgical intervention.	Biomarker for localizing epileptogenic focus
Tang et al.17	icEEG	3 epilepsy patients	Graph index complexity	Graph index complexity serves as an indicator of high-frequency oscillations in epileptic signal, and was able to successfully localize the epileptogenic zone.	Biomarker for localizing epileptogenic focus
Wilke et al.10	icEEG	2 neocortical intractable epilepsy patients	Outdegree	High correlation between regions with high outdegree and ictal onset regions.	Biomarker for localizing epileptogenic focus
Van Mierlo et al.18	icEEG	8 focal epilepsy patients who were seizure-free following resective surgery	Outdegree	During the first 20 s of seizure activity, the electrode with highest total outdegree was among the contacts involved in ictal onset.	Biomarker for localizing epileptogenic focus
Schindler et al.24	icEEG	60 patients with focal epilepsy	Zero-lag correlation	Zero-lag correlation of multichannel EEG decreases or remains unchanged during the first half of a seizure, followed by an increase prior to seizure termination.	Prediction of seizure onset
Takahashi et al.25	icEEG	3 TLE	L, C	No consistent topological characteristics found immediately prior to seizures. Consideration of brain states may be required for seizure prediction.	Prediction of seizure onset
Douw et al.21	MEG	17 patients with frontal or temporal lobe epilepsy secondary to glioma	C, L, γ, λ, σ, edge-weight correlation	Higher number of seizures immediately after resective surgery was associated with more increased θ-band edge-weight correlation, increased short-distance θ-band PLI, and increased long-distance intrahemispheric θ-band PLI. Associations were strongest within the temporal lobe and between the temporal lobe and other lobes.	Post-surgical seizure prediction

2. Lateralization and localization of epilepsy

Studies in TLE and other epilepsies based on graph theory metrics using various modalities have attempted to lateralize and/or localize epilepsy and are detailed below. Such analyses could potentially lead to more accurate surgical planning and better postsurgical outcomes. Although studies in fcMRI, surface EEG, and intracranial EEG (icEEG) have been performed, most localization attempts have used icEEG. In this section, we discuss which graph theory measures have been used thus far to characterize differences in TLE laterality or focus locality, and evaluate which measures appear to demonstrate the most potential as clinical biomarkers for laterality/localization.

2.1. FcMRI

Strength is a graph theoretic measure estimating the average magnitude of connectivity in a network. In lateralized TLE, strength was reduced in the ipsilateral hippocampus and parahippocampal gyrus compared to controls, indicating decreased overall connectivity of these regions to the rest of the brain, and providing a potential biomarker for lateralizing the epileptogenic focus.¹² Localization of whether the epileptogenic zone is medially or laterally located in the temporal lobe is also of interest. Another study has reported functional connectivity changes in regions affected by the epileptic process in TLE with a clinically defined medial focus, although a lateral TLE comparison group was not included. Specifically, mesial TLE (mTLE) was characterized by decreased connectivity in a large number of regions within the DMN and dorsal attention networks. Longer epilepsy duration has also been found to be associated with decreased connectivity between the right opercular inferior frontal gyrus and left triangular inferior frontal gyrus.¹³ It should be noted that the subject population in this study consisted of bilateral TLE, unlike the more common unilateral TLE seen in clinical practice, limiting generalization.

2.2. Surface EEG

Analysis of band power, synchronization and network measures in surface EEG of left TLE brain networks compared to controls has revealed marked differences in the θ- (4–7 Hz) and high α- (10–13 Hz) bands globally. In the θ-band, which is associated with hippocampal function, increased clustering coefficient (local processing), increased small-world index, and a trend toward a regular network were observed. In the high α-band, decreased clustering coefficient, decreased small-world index, and a trend toward random network were observed.¹⁴ These findings were seen globally over the brain, with differences in the θ-band primarily in the parietal and central electrodes and differences in the high α-band in the frontal and occipital electrodes, and suggests that pathology in left TLE is not restricted to medial temporal regions. A right TLE comparison group was not studied to evaluate whether these findings are particular to left TLE.

2.3. IcEEG

Studies of icEEG-based graph theoretic analysis have predominantly been in neocortical epilepsy in the interictal and ictal phases. As direct cortical recordings provide a unique window into epilepsy, these are reviewed here.

During the ictal and interictal phases in patients with neocortical epilepsy, nodes, defined as icEEG contacts, have been divided into active and inactive areas using the measure of betweenness centrality, which was found to reliably identify the clinically determined resected epileptogenic zones. The reliability of this measure was increased at higher frequencies, especially in the high γ-band (see Box 1 and Fig. 2),¹⁵ although research is needed as to whether this finding is applicable in mesial TLE and when extratemporal neocortical epilepsies are excluded. This study showed that betweenness centrality is an important variable to consider in identifying the epileptogenic zone during the ictal and interictal periods, although a higher spatial variance was noted interictally. The authors have proposed that the ability to identify the epileptogenic zone interictally could obviate the need for prolonged icEEG monitoring to capture seizures. Patients who remained seizure-free after resection were also found to have a greater number of “active” nodes in the gamma band resected than patients who continued to have seizures.¹⁵

Box 1. Clinical vignettes.

Clinical vignettes from published literature are presented that show some of the potential clinical applications of graph theoretic analysis.

1. Seizure localization

Wilke et al. applied graph theory methods to identify critical network nodes in cortical networks identified by ECoG in the interictal and ictal states. The graph measure of “betweenness centrality” was found to correlate with the identified epileptogenic zone that was resected in patients who were seizure-free following surgery. High frequency gamma activity had the best correlation with post-surgical seizure freedom, among the different frequencies analyzed (theta, alpha, beta, gamma).¹⁵ The following figure shows the identified ictal networks in the theta, alpha, beta and gamma frequency bands identified using K-means clustering of betweenness centrality metrics (blue regions). This corresponds to the seizure onset zone identified by the epileptologist (red regions) (Fig. 2).

2. Connectivity maps

Graph theory metrics can be used to create connectivity maps that emulate anatomic imaging such as MRI. Constable et al. show a “degree map”, which provides a voxel-by-voxel representation of the graph measure of degree. When laid out in the form of a map, the resultant gray-scale contrast image has the potential to show abnormal functional connectivity of particular regions of the brain⁵³ (Fig. 3).

3. Biomarker discovery

The field of machine learning uses statistical algorithms to detect patterns in data which may be used for biomarker discovery in personalized medicine. Graph theory metrics can be used as feature inputs into such algorithms, in order to contribute to biomarker discovery for diagnosis, prognosis, and prediction of treatment outcome. van Diessen et al. illustrate the potential utility of such an approach, demonstrating that graph theory measures of interictal surface EEG data can used to achieve high sensitivity and specificity in the diagnosis of partial epilepsy.⁵⁴ Using graph theory measures including degree centrality, path length, and various measures of centrality, they develop a diagnostic prediction model with sensitivity of 0.96, sensitivity of 0.95, and an overall excellent discriminative power of 0.89 based on area under the receiver operating characteristic curve (Fig. 4).

Fig. 2.

The betweenness centrality calculated in the (A) theta, (B) alpha, (C) beta, and D) gamma frequency bands during a representative seizure in a patient. The identified activated nodes are shown in blue, whereas the cortical regions marked in red correspond to the seizure onset zone identified by the epileptologist (image reproduced with permission from Wilke et al.¹⁵). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

“Visibility graphs” are a recently developed temporal graph theory method where, rather than using electrodes as the nodes of a graph, graph estimates for each icEEG electrode are obtained.¹⁶ Measures of the complexity of the time series at each electrode, such as graph index complexity or power of scale freeness, can be computed to distinguish electrodes with unusually high complexity. Such methods were applied to the high frequency sub-band from depth electrode recordings in three patients with epilepsy, enabling identification of the seizure focus based on the electrode with a significantly different level of graph-index complexity.¹⁷ Data from this study suggests that the seizure focus experiences an unusually high degree of complexity of its oscillatory patterns. However, the exceedingly small sample size of this study limits the generalizability of these findings, and further research is required to validate these preliminary findings.

An evaluation of the outdegree, which identifies network nodes that act as sources of information flow in a network, of graphs constructed during seizures in neocortical epilepsy found that regions with high outdegree agreed with the clinically determined seizure onset zones.¹⁰ In a similar study, it was found that the electrode contact with the highest outdegree during effective connectivity analysis of the first twenty seconds of ictal rhythmic icEEG activity in focal epilepsy was consistently among the contacts identified by epileptologists as the ictal onset, and always lay within the resected brain region.¹⁸

2.4. Summary

Data from fcMRI, surface EEG, and icEEG suggest that functional hub measures, or graph theory metrics which indicate regions crucial to information flow in the network such as betweenness centrality, graph index complexity, and outdegree, are potential biomarkers to localize TLE. Although most localization attempts have used icEEG, fcMRI and surface EEG have also yielded useful findings about the topology of subforms of TLE, including mesial and left TLE, which should be explored in the context of a comparison with lateral and right TLE, respectively. Additionally, graph theoretical analyses focusing on localization have been primarily based on functional data sources. Graph properties based on structural data sources, such as magnetic resonance imaging (MRI) or DTI, require further investigation.

2.5. Potential clinical use

Application of graph theory analysis to different modalities can be expected to help improve localization of temporal lobe epilepsy, leading to more precise resection of the epileptogenic cortex and sparing of normal tissue resulting in improved clinical outcomes. Promising topologic measures in this regard appear to be (1) strength (mean absolute correlation), found to be reduced in epileptogenic cortex,¹² and (2) betweenness centrality, found to correlate with the resected epileptogenic zone.¹⁵ Box 1 shows specific instances from the literature exemplifying the potential clinical applications of graph theory analyses to improved focus localization.

3. Prediction of pre- and post-surgical seizure occurrence and cognitive performance

A few studies have examined graph theoretical measures that can predict seizure freedom and cognitive performance following surgery, in addition to pre-ictal network topology characteristics that can predict seizure occurrence and hence be used to prevent seizures.

3.1. Structural MRI

Using MRI-based cortical thickness measurements, a more regular topology, consisting of increased clustering coefficient and path length (i.e., increased local processing and global integration), has been found to be associated with less post-surgical seizure freedom.¹⁹

3.2. DTI

Using DTI graph metrics, patients with TLE who were not seizure-free following resective surgery were found to have lower small-worldness in the ipsilateral temporal lobe subnetwork (higher integration at the expense of segregation), compared to patients who were seizure-free following surgery.²⁰

3.3. MEG

In patients with frontal or temporal lobe epilepsy secondary to glioma, magnetoencephalography (MEG) found no significant change in θ-band clustering coefficient (localized processing), characteristic path length (global integration), small-world index, or edge weight correlation (higher local synchronizability) immediately post-surgery versus six months post-surgery. A higher number of seizures immediately following surgery in these patients was associated with increased θ-band edge weight correlation. Although not statistically significant, a trend toward an association between higher number of seizures and longer θ-band path length (i.e., decreased global integration) was also found. Higher number of seizures directly after neurosurgery was also associated with both increased short-distance θ-band phase lag index (PLI) and increased long-distance intrahemispheric θ-band PLI, although these associations were lost at six months after neurosurgery. These associations were strongest within the temporal lobe and between the temporal lobe and other lobes, including temporo-occipital and fronto-temporal relations. No association was found between long-distance interhemispheric θ-band PLI and number of seizures immediately after neurosurgery.²¹ These results demonstrate that, directly after surgery, a higher number of seizures is associated with increased short-distance and intrahemispheric long-distance θ-band synchronizability within and with the temporal lobe.

3.4. Surface EEG

A simulated model of an acute surgical lesion using sodium amobarbital injection in patients with pharmaco-resistant TLE showed a shift toward a more random topology with decreased clustering coefficient (decreased localized processing) in all bands and lower path length (increased global integration) in the θ- and lower α-bands in surface EEG. There was also evidence of suboptimal information transport after injection, as evidenced by a decreased edge weight correlation in the theta and beta bands.²² Increased θ-band small-world index (i.e., more ordered network) and longer path length (i.e., decreased global processing) in the upper α-band were associated with better memory score in the acute post-injection period.²²

3.5. IcEEG

One application of graph theory is the evaluation of pre-ictal network topology that can be used to predict and prevent seizure onset. In this section, we review icEEG-based studies which have used graph theory metrics to quantify estimates of hypersynchrony. In addition, icEEG-based correlation maps have provided useful insight into hypersynchrony, which are reviewed here.

Seizures are classically thought to be a state of neuronal hypersynchrony, defined as either spatial hypersynchrony, where the amplitude of EEG signal is correlated across space, or localized hypersynchrony, where neurons fire collectively, leading to high amplitude action potentials. Assortativity, which measures the tendency of nodes to connect to other nodes with a similar degree, has also been found in patients with focal seizures to be associated with progression of the ictal period. In one study, assortativity was found to be decreased during the interictal phase, followed by an increase during seizures, which reaches a maximum immediately prior to seizure termination.²³ Another study using multichannel icEEG recordings found evidence of spatial decorrelation during the first half of seizure onset, followed by spatial hypersynchrony, defined as an increase in spatial zero-lag correlation of multichannel icEEG electrodes, prior to seizure termination in focal epilepsy.²⁴ It has been hypothesized that the increase in spatial correlation immediately prior to seizure termination may reflect a neural mechanism for seizure termination, whereas the decrease at ictal onset reflects the time-lagged propagation of information from the epileptogenic site.²⁴ Using long-term electrocorticography (ECoG) (39–76 h) in TLE, another study has found that brain states distinct from the sleep/wake cycle may also have an impact on seizure prediction.²⁵

Several possible interpretations have been postulated to explain the temporal pattern of connectivity changes during the interictal–ictal transition.²⁴ One possible explanation is that ictal seizure spreading causes spatial decorrelation by differences in axonal conduction times causing the summation of locally hypersynchronous neuronal discharges to cancel out over space. Another possible explanation is that decorrelated neuronal activity induces seizure spreading. Alternatively, a mixture of the two events may occur, where decorrelated neuronal activity induces seizure spreading, which induces further decorrelation. This is supported by clinical observations, in which seizure propagation follows an exponential time course.²⁴

3.6. Summary

Data suggest that graph theory metrics which quantitate hypersynchronizability are of clinical utility in predicting post-surgical seizure recurrence. Since edge weight correlation measures the degree to which connections to a region have similar weights, it provides a measure of local synchronizability. Similarly, PLI measures the strength of the interdependencies between the EEG signals at different electrodes, which may also be interpreted as a measure of synchronizability. MEG findings point to the validity of edge weight correlation and PLI as hypersynchronizability measures which can be used as reliable predictors for post-surgical seizure recurrence. The associations found between PLI and postsurgical seizure frequency indicate that hypersynchronizability with and within the temporal lobe may play a role in post-surgical seizure recurrence. In addition, increased network regularity using structural MRI was found to be associated with post-surgical seizure recurrence in the form of increased local connections and decreased global connections. Increased regularity may reduce the number of parallel backup routes available after resection of important hubs through neurosurgery, leading to the formation of abnormal epileptogenic connections.

Interestingly, although increased path length (decreased global integration) was found to be associated with poor post-surgical seizure outcome with respect to seizure frequency using both structural MRI and MEG studies, it was also associated with better memory score acutely after injection of sodium amobarbital using surface EEG. However, this finding has not been conclusively established in the literature. An fMRI study, for example, has found evidence that, in healthy subjects, higher intelligence quotient (IQ) is associated with shorter path length in low frequency ranges.²⁶ Discrepancy between these studies may be attributable to a variety of factors, including differences in population, differences in cognitive tests utilized, or differences in modality.

IcEEG data indicates that graph theory metrics which measure synchronizability, such as correlation and assortativity coefficient, have potential utility as markers for predicting pre-surgical seizure occurrence. Differences in the information contained in these measures, as well as other measures of synchronizability, should be exploited to seek predictive models which incorporate the most informative combinations of measures to predict seizure onset. These findings collectively reveal a functional reorganization of the brain networks during seizures which may be used to create predictive models for seizure occurrence. Analysis of such networks is made more tractable using the principles of graph theory.

3.7. Potential clinical use

With the development of neurostimulation devices such as responsive neurostimulation (RNS), there is tremendous interest in seizure prediction algorithms. Graph theory analysis may provide a method to develop more reliable algorithms that can then improve seizure control. Promising topologic measures in this regard appear to be edge weight correlations and PLI.

4. Cognitive decline

TLE is associated with cognitive decline^27–30 that likely results from effects of epilepsy on local and remote brain regions.^31,32 Graph theory provides a useful method of investigating the network mechanisms behind cognitive decline in TLE, by exploring changes in network topology that may be conducive to or result from neuronal loss. Consequently, these topological measures may be used to track the progression of cognitive decline in TLE.

4.1. Structural MRI

Although MRI-based cortical thickness measurements in both TLE patients and controls have found a small world topology, TLE cortical networks followed a more regular configuration,¹⁹ which has been associated with decreased resilience to pathologic attack.³³ Specifically, TLE patients have a higher vulnerability to “targeted attacks” (i.e., when brain regions with the highest impact on information flow in the brain were removed), despite being as robust to “random attacks” (i.e., when randomly selected brain regions were removed) as controls. This suggests that, compared to controls, TLE patients lack potential backup routes in the parallel organization of neuronal pathways¹⁹ which we postulate may be one mechanism for cognitive decline. Specifically, vulnerability to disease may be either a cause or consequence of TLE. It may also be a mixture of both, through a positive feedback loop in which vulnerability to pathological attack facilitates seizures, which induce excitotoxic neuronal atrophy resulting in the loss of backup routes and further vulnerability to attack. Additionally, the study found evidence of increased path length (i.e., decreased long-range connectivity) in TLE patients, indicating decreased global efficiency of information transfer in TLE¹⁹ and lending itself as a potential explanatory factor for the cognitive decline observed in TLE. An increase in clustering coefficient was also identified,¹⁹ which may result from the compensatory formation of aberrant local connections in response to a decrease in the number of long-range connection.

4.2. DTI

Frontal and temporal lobe epilepsy patients with severe cognitive impairment were found to possess brain networks with lower clustering coefficient and increased path length compared to patients with mild cognitive impairment and healthy controls, signifying decreased local processing as well as global integration. These changes were amplified with lower full scale IQ indicating that the mechanism of cognitive decline in TLE is by decreased local as well as global deep white matter connections. However, the whole brain white matter was preserved in TLE patients,³⁰ suggesting that it is not a macrostructural decrease in white matter volume that is responsible for the cognitive decline in TLE, but rather microstructural changes due to neuronal loss or compensatory mechanisms.

4.3. FcMRI

FcMRI has corroborated the association found by DTI between decreased local and global connections with cognitive impairment. Using fcMRI, the same group of frontal/temporal lobe epilepsy patients with severe cognitive impairment was found to have a lower clustering coefficient compared to patients with mild cognitive impairment and healthy controls, as well as increased path length compared to healthy controls. Within the frontal/temporal lobe epilepsy patient population itself, decreases in the level of clustering coefficient were also found to be associated with decreased cognitive performance.²⁹ This indicates a positive correlation between the IQ, as measured by the full scale IQ test/IQ discrepancy score, and the ability to perform local specialized information processing as well as serial information processing. The association between path length and intellectual performance has been confirmed by other studies as well.²⁶

4.4. Summary

Overall, structural and functional neuroimaging studies have both found evidence of an association of cognitive impairment with lower clustering coefficient and longer path length.^26,29,30 The agreement between these studies implies that decreased localized as well as global information processing play a role in the mechanism of cognitive decline in TLE, and that these graph theory measures may have clinical utility in tracking its progression.

4.5. Potential clinical use

Developing an objective neuroimaging or electrophysiological biomarker for neuropsychologic performance would improve the assessement and prognostication of cognitive function in TLE. Further studies can also evaluate whether this information would be helpful in the triage for early epilepsy surgery.

5. Limitations of graph-theoretical analysis

Although a graph-theoretical approach to understanding structural or functional brain networks in TLE is advantageous in many respects, there are several difficulties particular to this form of analysis which should be taken into account. Due to the large number of regions and graphical measures tested using hypothesis testing, typical multiple comparison procedures may lead to an overly conservative threshold with a high probability of Type II errors, which may be addressed through a priori restriction of clinical hypotheses.³⁴ Additionally, studies, even if performed on the same population, are subject to differences in graph construction rules. The decision to use binary or weighted networks has a strong impact on findings, as different construction rules have different limitations, including threshold choice, unconnectedness, or link-density.³⁵ One possibility is to apply different construction rules when performing graphical analyses in order to evaluate whether findings are robust between them. Evaluation of graph theoretic findings to draw clinical conclusions presents another difficulty, due to ambiguity in discerning whether network changes are a cause or consequence of seizures. Many studies also differ with respect to antiepileptic drug usage within their study samples, and their effects on network structure are not known.

Our review of the graph theory literature in TLE shows specific existing discrepancies. In particular, there has been some variation in the reported alteration of clustering coefficient for the TLE network: both increases^19,35–37 and decreases^13,29,30 have been identified. One possible clue for explaining these inter-study differences comes from neuronal graph theory models, which have shown clustering coefficient to increase during most of the sclerotic process, and decrease in the final stages.³⁸ Additionally, study populations with increased drug load have been found to experience decreased levels of clustering coefficient.³⁹ Mean estimates of clustering coefficient are also positively correlated with the sample variance of the clustering coefficient,⁴⁰ so that studies with greater sample variance in clustering coefficient are more likely to experience higher group-level estimates of clustering coefficent. Other reasons may include sample size and study population variability, as well as difference in anti-epileptic drug (AED) regimens. Also, significantly, different modalities (e.g., DTI, fMRI, EEG, MEG) may examine different aspects of connectivity, and may not be comparable in all aspects. Additional research is needed to investigate whether these factors may have an impact on the calculation of various graph topological measures. Similarly, although characteristic path length is generally observed to be increased in TLE,^29,41,35,42 one fMRI study has reported a decrease in TLE.¹³ The subject population of this study was composed of bilateral mTLE patients only, and we speculate that the network topology differences between bilateral TLE, and the more common unilateral TLE, may account for discrepant findings in this study.

6. Conclusions and future directions

A rapidly growing body of evidence highlights the clinical potential of graph theoretic methods for diagnostic and predictive purposes in TLE. We have provided a review of the current state of multi-modal findings on graph theory metrics which may be clinically useful in the development of statistical models for localization and predictive purposes. Formulation of statistical models with high sensitivity and specificity are needed to integrate the graph theory measures identified in this study with other potential distinguishing variables, in order to provide better clinical tools for diagnosis and prediction. In particular, there is a need for prediction models based on multivariate classifiers. By capturing various aspects of the network structure of TLE, utilization of multivariate methods based on graph theory is likely to allow for greater predictive ability than prediction based only on single metrics.

Another need is for integrative analysis of data from multiple modalities. This would allow for mitigation of Type I or Type II errors induced by predictive models based solely on unimodal data. The disadvantages present in one modality may not be present in another, and integration of findings from multiple modalities may resolve current inter-/intra-modality discrepancies by allowing data from different modalities to inform each other. These developments require collaboration between the fields of statistics and neurology to form clinically useful models with good predictive ability.

Fig. 3.

Gray-scale short axis MR images (from 42 healthy controls) with contrast reflecting the functional connectivity of each voxel as measured by the network measure of degree (brighter colors indicate higher degree). Such maps can be obtained for individual patients and compared to control-group data to isolate tissue elements with abnormal functional connectivity (image reproduced with permission from Constable et al.⁵³).

Fig. 4.

ROC curve (dark blue) and 95% confidence interval for the network characteristics based on the broadband frequency (image reproduced with permission from van Diessen et al.⁵⁴). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Abbreviations

TLE

temporal lobe epilepsy

DTI

diffusion tensor imaging

fcMRI

functional connectivity magnetic resonance imaging

EEG

electroencephalography

icEEG

intracranial electroencephalography

mTLE

mesial temporal lobe epilepsy

MRI

magnetic resonance imaging

MEG

magnetoencephalography

DMN

default motor network

PLI

phase lag index

IQ

intelligence quotient

ECoG

electrocorticography